Momentum-resolved visualization of electronic evolution in doping a Mott insulator

High temperature superconductivity in cuprates arises from doping a parent Mott insulator by electrons or holes. A central issue is how the Mott gap evolves and the low-energy states emerge with doping. Here we report angle-resolved photoemission spectroscopy measurements on a cuprate parent compound by sequential in situ electron doping. The chemical potential jumps to the bottom of the upper Hubbard band upon a slight electron doping, making it possible to directly visualize the charge transfer band and the full Mott gap region. With increasing doping, the Mott gap rapidly collapses due to the spectral weight transfer from the charge transfer band to the gapped region and the induced low-energy states emerge in a wide energy range inside the Mott gap. These results provide key information on the electronic evolution in doping a Mott insulator and establish a basis for developing microscopic theories for cuprate superconductivity.


Supplementary Note 1. Sample charging effect test
In the photoemission process, electrons in the measured sample are kicked out by the incident light. The escaped electrons are compensated by electrons flowing into the sample from the grounding, keeping the sample constantly in an electrically neutral condition. This compensation process can be readily realized in good conducting materials. However, when the sample is a poor conductor or an insulator, the electrons flowing from the grounding to the sample are blocked and may not be sufficient to compensate the lost electrons in the photoemission process, causing an accumulation of positive charges on the sample. The positive charges will attract the out-going photoelectrons, reducing their kinetic energy that corresponds to an energy shift to higher binding energy in the measured photoemission spectrum. Such a charging effect depends on the conducting property of the sample and the incident photon flux. Poor conductivity of the sample and large photon flux will result in a more serious charging effect. To carry out normal photoemission measurement and get intrinsic signal from a less-conductive sample, one should try to avoid the sample charging problem by reducing the photon flux, or maintaining a relatively high conductivity by measuring the sample at high temperature.
The Ca 3 Cu 2 O 4 Cl 2 (CCOC326) sample is a perfect insulator which makes the photoemission measurements challenging. To avoid the sample charging effect, it is preferable to measure the sample at high temperature. On the other hand, for our present Rb-deposition measurements, in order to have sufficient Rb absorption on the sample surface to introduce electron doping over a relatively wide range, the sample needs to be measured at lower tem-2 perature. To compromise between the charging effect and the Rb deposition efficiency, we tested the sample charging effect at different photon flux and at different temperatures, as shown in Supplementary Fig. 1. We find that the charging effect is negligible when the sample is measured at 50 K and above ( Supplementary Fig. 1b). Then we chose the sample temperature around 50 K during our measurements. We note that, since CCOC326 is more conductive than its single-layer counterpart Ca 2 CuO 2 Cl 2 (CCOC214), this makes it possible to measure CCOC326 at much lower temperature than that for CCOC214. This is critical to the success of the experiment to realize sufficient and stable Rb absorption on the CCOC326 sample surface for electron doping. During the measurements, we frequently varied the photon flux to make sure that little charging effect is present in all the measurements.  Fig. 2b and Supplementary Fig. 2c) lies at ∼0.3 eV below the Fermi level. The charge transfer band near (-π,0) is much weaker in its intensity than that at the (π/2,π/2) nodal point and its EDC peak position lies at a higher binding energy, as shown in Supplementary Fig. 2f. As soon as we deposit Rb on the CCOC326 sample surface, we started to see spectral weight at higher kinetic energy above the initially observed bands 4 in pristine CCOC326. These newly-developed spectral weight gets stronger with increasing Rb deposition, as seen in Supplementary Fig. 3. Surprisingly, the new states lie above the Fermi level position that is determined for the pristine CCOC326 from the usual gold Fermi cutoff measurement. Such Rb deposition process were repeated a couple of times, the measured results are highly reproducible. We note that, after each Rb deposition stage, the measured data along three momentum cuts are stable against the photon flux and measurement time. Little sample charging effect was involved in all the measurements.
The measured data show clear momentum dependence; they behave quite differently along the three momentum cuts. They also exhibit systematic variation with Rb deposition. We checked on the well-studied samples, like Bi 2 Sr 2 CaCu 2 O 8 , to make sure that our ARPES system works in a normal condition. In particular, we find that the measured data show similarity to the electron-doped (Nd,Ce) 2 CuO 4 data[2] at relatively high doping. These observations indicate that the measured data are intrinsic to the measured sample; they are not from experimental artifacts.
Since photoemission measures only the occupied state because of the Fermi cutoff, the observation of states well above the "Fermi level" of the pristine CCOC326 indicates that the real Fermi level for those measurements after Rb deposition lies at higher kinetic energy. At least it should be higher than that of the observed states.
The usual way of determining the sample Fermi level is no longer useful for the Rb-deposited CCOC326, we have to find another way of setting the Fermi level. We found that the overall electronic structure evolution 5 with electron doping in our present case is similar to that in electron-doped (Nd,Ce) 2 CuO 4 [2]. In (Nd,Ce) 2 CuO 4 with different electron doping levels (0, 0.04, 0.10 and 0.15), the Fermi level was determined from the usual way of measuring the gold Fermi cutoff. Particularly, the states near the antinodal (π,0) point approach the Fermi level for the doped samples [2]. We also find that the antinodal states in Rb-deposited CCOC326 lie at higher kinetic en- The observation in Supplementary Fig. 3 that electronic states are detected above the normal Fermi level from gold is very rare in ARPES measurements. This could be due to the special case that the measured insulating sample surface is deposited with Rb. With Rb deposition, the top layer(s) of the sample surface is doped with electrons. But the sample beneath the electron-doped layer(s) remains insulating as before. Therefore, it is possible 6 that there is a band-bending between the top electron-doped layer(s) and the underneath insulating layers that gives rise to the Fermi level difference between the two parts. Although the exact origin of the Fermi level difference needs further investigations, we note that the data in Supplementary   Fig. 3 are intrinsic and highly reproducible. Since we are dealing with relatively large energy scale change with doping in the present work, the slight uncertainty in the Fermi level will not affect our main results and conclusions. [2] Armitage, N. P. et al. Doping dependence of an n-type cuprate superconductor investigated by angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 88, 257001 (2002).